But what the hell does it ?
I checks the outgoing and the ingoing voltage.
If the ingoing is lower then the outgoing it shuts down.

What does that mean?
It's simple, if stuff with electricity touches water it shuts off the power.

Why do i tell that?
That photo was made in germany.
Every german bathroom has an rcd, thats why you can't kill yourself with a toaster taking a bath.
So if they used a power point in a bathroom, nothing is going to happen.

In my country, the current breakers (I believe it's called like that, in French : Disjoncteur Différentiel Résiduel) have a breaking current of 30 mA.
Then, if an electric installation is protected with a DDR (or RCD I think it is), how come people die from electricity at home every day ? (I'm not criticizing or anything, just asking the question ! I'm curious).

It actually checks the CURRENT difference between the output's phase and neutral. If it exceeds a set amount (for eg. 10mA, 30mA, etc.) by for eg. touching the phase wire, allowing the electricity to flow through your body into neutral (earth) instead of the circuits neutral wire, it disengages, saving your pathetic life. Or something like that, i don't know.